In a saucepan, combine the sugar and the water over median heat and bring to a boil, stirring until the sugar dissolves. Cook until a thin syrup forms, 4 to 5 minutes.

Add the plums and continue to cook, stirring often, until the plums soften, another 4 to 5 minutes. Stir in the vanilla. Remove from the heat, cover to keep warm, and set aside.

In a shallow baking dish, combine the eggs and water or milk and beat them lightly.

Add the bread in a single layer, soaking the first side 1 to 2 minutes, then turning and soaking the other side.

In a large frying pan, melt the butter over medium heat until it foams. Add the bread and cook until golden, 3 to 4 minutes. Turn with a spatula and cook the other side until golden, another 3 to 4 minutes.

Put one piece of the bread on each of 4 plates. Over each, spoon some of the warm plums and their sauce and sprinkle with a little confectioner's sugar. Serve immediately.